Multiply a monomial and a polynomial

1
Multiply a monomial and a polynomial
Example 1
Find the product
Solution
2
Multiply polynomials using an area model
Example 2
Write a polynomial for the area of the model
shown.
Solution
You know that the area of a rectangle is the
product of its length and width. In the model,
let ________ represent the length and let
________ represent the width. To find the total
area of the model, ____ the areas of each
rectangular part.
____ ____ ____ ____ ____ ____
____ ____ ____ ____ ____
____ ____ ____
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Checkpoint. Complete the following exercises.
1. Find the product
4
Checkpoint. Complete the following exercises.

• The dimensions of a rectangle are 4x 1 and x
  2. Draw an area model. The write an expression
  for the area of the rectangle.

5
Multiply polynomials horizontally
Example 3
Find the product
Solution
6
Multiply binomials
Example 4
Find the product
Solution
7
Checkpoint. Find the product.
8
Multiply binomials by using F O I L.
9
Checkpoint. Find the product.
10
Checkpoint. Find the product.
11
Multiply polynomials using a volume model
Example 5
Write a polynomial for the volume of the
rectangular prism shown.
Solution
You know that the volume of a rectangular prism
is the product of its_______, _______ and
________. In the figure shown, let ___ represent
the length, let ________ represent the width and
let ________ represent the height.
height
length
width
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Multiply polynomials using a volume model
Example 5
Write a polynomial for the volume of the
rectangular prism shown.
Solution
____(______)(______)
_______(___) ___(___) ___(___) ___(___)
____(____ ____ ____ ____)
____(_______________)
___________________________
___________________________
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Checkpoint. Complete the following exercises.

• Write an expression for the volume of the prism
  shown.

____(______)(______)
____(____ ____ ____ ____)
____(_______________)
__________________
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